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Question Number 208533 by alcohol last updated on 18/Jun/24
z′ = (1/2)(z+(1/z))  z and z′ are complex numbers  show that z = 2e^(iθ)   show that M′ describes a conic section
$${z}'\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left({z}+\frac{\mathrm{1}}{{z}}\right) \\ $$$${z}\:{and}\:{z}'\:{are}\:{complex}\:{numbers} \\ $$$${show}\:{that}\:{z}\:=\:\mathrm{2}{e}^{{i}\theta} \\ $$$${show}\:{that}\:{M}'\:{describes}\:{a}\:{conic}\:{section} \\ $$
Answered by Berbere last updated on 18/Jun/24
what is z complexe    n plane?%
$${what}\:{is}\:{z}\:{complexe} \\ $$$$ \\ $$$${n}\:{plane}?\% \\ $$
Answered by Berbere last updated on 18/Jun/24
z′=(1/2)(z+(1/z)) z=2e^(iθ)   incomplet information we can just say z#0
$${z}'=\frac{\mathrm{1}}{\mathrm{2}}\left({z}+\frac{\mathrm{1}}{{z}}\right)\:{z}=\mathrm{2}{e}^{{i}\theta} \\ $$$${incomplet}\:{information}\:{we}\:{can}\:{just}\:{say}\:{z}#\mathrm{0} \\ $$$$ \\ $$

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